Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I: Abstract Theory
Atsushi Yagi
The classical Łojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Łojasiewicz–Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Łojasiewicz–Simon gradient inequality.
In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction–diffusion equations with discontinuous coefficients, reaction–diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller–Segel equations even for higher-dimensional ones.
In order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Łojasiewicz–Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction–diffusion equations with discontinuous coefficients, reaction–diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller–Segel equations even for higher-dimensional ones.
Categorie:
Anno:
2021
Edizione:
1st ed. 2021
Casa editrice:
Springer
Lingua:
english
Pagine:
71
ISBN 10:
981161895X
ISBN 13:
9789811618956
Collana:
SpringerBriefs in Mathematics
File:
PDF, 576 KB
IPFS:
,
english, 2021
Amazon 
Barnes & Noble 
Bookshop.org 
Converti i file
Più risultati di ricerca
Altri vantaggi 
Termini più frequenti
Liste di libri correlati
